What is the simplest radical form of the square root of 108?

What is the simplest radical form of the square root of 108?

• A. 6 radical 4
• B. 6 radical 3
• C. 9 radical 3
• D. 3 radical 12

Answer: (B)

To find the simplest radical form of the square root of 108, we first need to factor 108 into its prime factors. The number 108 can be expressed as follows: 108 = 36 × 3 = (6 × 6) × 3 = (2 × 3)² × 3. From this factorization, we can identify the square factors. The square of 6 (which is 6²) can be taken out of the square root: √108 = √(36 × 3) = √36 × √3. Since √36 equals 6, we can simplify further: √108 = 6√3. This form, 6√3, is indeed the simplest radical form as it has no further simplifications. Thus, the answer correctly is 6 radical 3, capturing both the entire factorization and the appropriate simplification process.

To find the simplest radical form of the square root of 108, we first need to factor 108 into its prime factors. The number 108 can be expressed as follows:

108 = 36 × 3 = (6 × 6) × 3 = (2 × 3)² × 3.

From this factorization, we can identify the square factors. The square of 6 (which is 6²) can be taken out of the square root:

√108 = √(36 × 3) = √36 × √3.

Since √36 equals 6, we can simplify further:

√108 = 6√3.

This form, 6√3, is indeed the simplest radical form as it has no further simplifications. Thus, the answer correctly is 6 radical 3, capturing both the entire factorization and the appropriate simplification process.